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Home » So \( a, b = 1, 3 \) (up to order), both real. - DNSFLEX

So \( a, b = 1, 3 \) (up to order), both real. - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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First, factor the denominator:
n^2 + 3n + 2 = (n + 1)(n + 2)
So the general term is:
a_n = rac{1}{(n + 1)(n + 2)}
We apply partial fraction decomposition:
rac{1}{(n + 1)(n + 2)} = rac{A}{n + 1} + rac{B}{n + 2}
Multiplying both sides by \((n + 1)(n + 2)\):
= A(n + 2) + B(n + 1)
Setting \( n = -2 \):
\( 1 = B(-1) \Rightarrow B = -1 \)

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